Strictly face-regular spheres

All strictly face-regular two-faced polyhedra are organized in 68 sporadic ones and 3 infinite families prisms Prism, (b 5), antiprisms APrismt (b 4), and snub Prismb (b 6). 

A sphere is called 2-isohedral if its symmetry group has two Dibits of faces. All 41 2-isohedral two-faced polyhedra (so, amongst those 71) are identified. They are given with symmetry groups and constructions. 

The three infinite families are represented as Nrs. 15, 44, and 61 in Table 9.1, by their smallest members. Nrs. 2, 18 of Table 9.1 can be seen as snub Prism3, snub Prism4. Now, Prism, APrism, snub Prisms are Platonic polyhedra. Prisms is given separately under Nr. 1 and not as a case in Nr. 15 of Prism, because it has a 4. 

Theorem 9.1.1 The list of strictly face-regular 3-connected ( a, b], k)-spheres aRu bRj is the one of Table 9.1. 

All elliptic ( a, b], fc)-spheres, i.e. those with 2k b(k — 2) are listed in Chapter 2, we can just pick them here. All five there, having no 2-gons, are strictly face-regular. 

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We classify only the strictly face-regular spheres and strictly face-regular normal balanced planes. The plane case contains the toms case as a subcase. For the plane, the Euler formula does not hold, but the condition of normality, discussed thereafter,... 

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